Unified Theory of Topological and Geometric Problems in Mechanical Design and Manufacturing

该基金将为机械产品设计和制造中描述和解决几何和拓扑问题的理论基础提供支持。将发展一个理论，以涵盖一个分类和几何和拓扑问题的一般类别的形态学，他们的特征，和他们各自的可解性条件。该理论将提供通用解决方案技术的范围和局限性的理解。统一的特征将包含多个抽象层次的拓扑和几何实体的表示，一组标准的拓扑和几何关系，以及一组最小的通用设计任务或问题。高级问题定义将以通用几何范例的形式编码，该范例不仅包含几何模板，还包含指定设计任务或目标的机制。将高级问题映射到低级标准几何任务的方法也将被研究。如果成功，这项研究将导致对不同领域几何问题的统一处理，并将加强产品设计过程中不同部分之间的整合。从长远来看，这个项目的结果有可能扩展CAD/CAM在上游（初步设计）和下游（制造计划）自动化设计和制造任务中的范围。这项研究也将有利于在整个产品开发过程中使用的不同计算机辅助设计系统之间交换参数几何数据的标准的发展，从而减少开发成本和上市时间。

This grant will provide support for developing theoretical foundations for describing and solving gometric and topological problems in mechanical product design and manufacture. A theory will be developed to encompass a taxonomy and morphology of generic classes of geometric and topological problems, their characterization, and their respective solvability conditions. The theory will provide an understanding of the scope and limitations of generic solution techniques. The unified characterization will contain representation of topological and geometric entities at multiple abstraction levels, a standard set of topological and geometric relations, and a minimum set of generic design tasks or issues. High level problem definitions will be encoded in the form of generic geometry exemplars that will contain not only geometry templates, but also mechanisms to specify the design task or goal. Methods for mapping high level problems to low level standard geometric tasks will also be investigated. If successful, this research will lead to a uniform treatment of geometric problems in diverse areas and will enhance integration between different parts of the product design process. In the long run, the results of this project have the potential to extend the scope of CAD/CAM in automating design and manufacturing tasks both upstream (preliminary design) and downstream (manufacturing planning). This research will also benefit the development of standards for exchange of parametric geometry data between different computer aided design systems used throughout the product development process, thus reducing development cost and the time to market.